Finite Group Databasebeta

← C2×#10591566 #11860078

Subgroups — C2×#10591566 #11860078

Order 1152.

1169 conjugacy classes of subgroups.

The subgroup lattice has 487 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic
3C2×Dic3×D12C211yesmaximal, characteristic
4C2×#63662C211yesmaximal, characteristic, complemented
5#10591566C218yesmaximal, direct product factor
6C2×#63575C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic
8C2×#63554C211yesmaximal, characteristic, complemented
9C2×#5164—31nomaximal
10C2×#5026—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×D3×Dic3—21no—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×Q8×Dic3—22no—
17C3×Q8×Dic3C2214yescomplemented
18C2×C3×#215C418yescomplemented
19C2×C3×#215C2214yes—
20C2×C3×C4⋊Dic3—21no—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3—21no—
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×(C2×D3)⋊Dic3—21no—
26Dic3×D12—22no—
27Dic3×D12C2214yes—
28#63662C2214yescomplemented
29#63575C2214yescomplemented
30#63562C2214yes—
31#63554C2214yescomplemented
32C22×C3×SD16—31no—
33C2×C3×C4×Q8—31no—
34C2×Q8×Dic3D311yescharacteristic, complemented
35C22×#215D311yescharacteristic
36C2×D4×Dic3—31no—
37C2×C4×D12—31no—
38C2×#835—31no—
39C2×#835—31no—
40C2×#835—61no—
41C2×#832—31no—
42#5164—38no—
43C2×#818—31no—
44C2×#815—31no—
45#5026—38no—
46C2×#809—31no—
47C2×#807—31no—
48C2×#803—31no—
49C23×C3×D3—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8—22no—
52C2×C32×Q8C2×C414yescomplemented
53C2×C32×Q8C2312yes—
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D411yescharacteristic
59C22×C3×Dic3D411yescharacteristic
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12C2×C414yes—
63C2×C3×D12C2312yes—
64C2×D3×Dic3—24no—
65C2×D3×Dic3—44no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)C2312yes—
68C2×C3⋊(C3⋊C8)—22no—
69C2×C3⋊(C3⋊C8)C2312yes—
70C3×#215C2×C4116yescomplemented
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—24no—
73C3×C4⋊Dic3C2312yes—
74C3×C4×Dic3—24no—
75C3×C4×Dic3D412yes—
76C3×C4×Dic3C2312yes—
77C2×C3×C3⋊C8C2×C414yescomplemented
78C2×C3×C3⋊C8C2312yes—
79(C2×D3)⋊Dic3—24no—
80C2×#440—91noSylow
81C22×C3×Q8—21no—
82C22×C3×Q8C2×D311yescharacteristic
83C22×C3×Q8C2×D311yescharacteristic
84C22×C3×D4—31no—
85C23×Dic3—61no—
86C22×D12C2×D311yescharacteristic
87C22×C4×D3—61no—
88C2×C3×SD16—38no—
89C2×C3×SD16—34no—
90C22×C3×C8—31no—
91C3×C4×Q8—34no—
92C3×C4×Q8—62no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—61no—
95C2×C3×C42—31no—
96C2×C3×C42—61no—
97C2×#217—61no—
98Q8×Dic3—22no—
99Q8×Dic3C2×D314yescomplemented
100C2×#215Dic318yescomplemented
101C2×#215C2×D314yes—
102D4×Dic3—34no—
103D4×Dic3—62no—
104C2×(C2×D3)⋊C4—61no—
105C2×C4⋊Dic3—21no—
106C2×C4⋊Dic3—31no—
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3—61no—
109C2×C4⋊Dic3C2×D311yescharacteristic
110C2×C4×Dic3—21no—
111C2×C4×Dic3C2×D311yescharacteristic
112C22×C3⋊C8—31no—
113C22×C3⋊C8—31no—
114C22×C3⋊C8—61no—
115C22×C3⋊C8C2×D311yescharacteristic
116C4×D12—34no—
117C4×D12—62no—
118#835—34no—
119#835—34no—
120#835—64no—
121#832—34no—
122#818—34no—
123#815—34no—
124#809—34no—
125#807—34no—
126#803—34no—
127C23×C32C2×D411yescharacteristic
128C22×C3×D3—24no—
129C22×C3×D3—22no—
130C22×C3×D3—42no—
131C22×C3×D3—42no—
132C32×Q8—24no—
133C32×Q8—22no—
134C32×Q8C22×C414yescomplemented
135C2×C32×C4—24no—
136C2×C32×C4—22no—
137C2×C32×C4C22×C412yes—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4112yes—
140C2×C32×C4C2411yescharacteristic
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—42no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—42no—
147C2×C3×Dic3C2×D412yes—
148C2×C3×Dic3C2×D412yes—
149C3×D12—24no—
150C3×D12—22no—
151C3×D12C22×C414yes—
152D3×Dic3—48no—
153C3⋊(C3⋊C8)—22no—
154C3×C3⋊C8C22×C414yescomplemented
155C22×SD16—31no—
156C2×C4×Q8—31no—
157C2×C4×D4—91no—
158#440—98no—
159C2×#107—91no—
160C2×#103—91no—
161C2×#102—91no—
162C2×#97—91no—
163C24×C3—61no—
164C23×D3—21no—
165C2×C3×Q8—22no—
166C2×C3×Q8—21no—
167C2×C3×Q8—22no—
168C2×C3×Q8—21no—
169C2×C3×Q8—24no—
170C2×C3×Q8—22no—
171C2×C3×Q8—42no—
172C2×C3×Q8—41no—
173C2×C3×Q8C4×D314yescomplemented
174C2×C3×Q8C2×Dic314yescomplemented
175C2×C3×Q8C22×D312yes—
176C2×C3×Q8C22×D312yes—
177C2×C3×D4—34no—
178C2×C3×D4—32no—
179C2×C3×D4—62no—
180C2×C3×D4—61no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—31no—
185C22×C3×C4—31no—
186C22×C3×C4—41no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C22×Dic3—21no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3—64no—
194C22×Dic3—121no—
195C22×Dic3—124no—
196C22×Dic3#6711yescharacteristic
197C22×Dic3#6711yescharacteristic
198C2×D12—21no—
199C2×D12—22no—
200C2×D12C2×Dic314yes—
201C2×D12C22×D312yes—
202C2×C4×D3—64no—
203C2×C4×D3—124no—
204C3×SD16—316no—
205C2×C3×C8—34no—
206C2×C3×C8—32no—
207C3×C4⋊C4—32no—
208C3×C4⋊C4—64no—
209C3×C4⋊C4—61no—
210C3×C42—32no—
211C3×C42—32no—
212C3×C42—64no—
213#217—64no—
214#215C2×Dic3116yescomplemented
215(C2×D3)⋊C4—64no—
216C4⋊Dic3—21no—
217C4⋊Dic3—24no—
218C4⋊Dic3—32no—
219C4⋊Dic3—32no—
220C4⋊Dic3—62no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223C4⋊Dic3—121no—
224C4⋊Dic3C22×D312yes—
225C4×Dic3—24no—
226C4×Dic3#6712yes—
227C4×Dic3C22×D312yes—
228C2×C3⋊C8—32no—
229C2×C3⋊C8—32no—
230C2×C3⋊C8—62no—
231C2×C3⋊C8—62no—
232C2×C3⋊C8—62no—
233C2×C3⋊C8—122no—
234C2×C3⋊C8C2×Dic314yescomplemented
235C2×C3⋊C8C22×D312yes—
236C22×C32C4×D412yes—
237C22×C32AGL(1,ℤ/8)12yes—
238C22×C32#13712yes—
239C22×C32C22×D411yescharacteristic
240C2×C3×D3—24no—
241C2×C3×D3—42no—
242C2×C3×D3—42no—
243C2×C3×D3—48no—
244C32×C4—24no—
245C32×C4C4×D412yes—
246C32×C4C23×C411yescharacteristic
247C32×C4C2×#4111yescharacteristic
248C3⋊Dic3—42no—
249C3×Dic3—22no—
250C3×Dic3—22no—
251C3×Dic3—42no—
252C22×Q8D3211yescharacteristic
253C22×D4—31no—
254C23×C4—181no—
255C2×SD16—38no—
256C2×SD16—34no—
257C22×C8—31no—
258C22×C8—91no—
259C4×Q8—34no—
260C4×Q8—62no—
261C4×D4—94no—
262C4×D4—182no—
263C2×C4⋊C4—31no—
264C2×C4⋊C4—61no—
265C2×C4⋊C4—91no—
266C2×C22⋊C4—181no—
267C2×C42—31no—
268C2×C42—61no—
269#107—94no—
270#103—94no—
271#102—94no—
272#97—94no—
273C23×C3—21no—
274C23×C3—64no—
275C23×C3—62no—
276C23×C3—122no—
277C23×C3—122no—
278C23×C3D3×D411yescharacteristic
279C23×C3C2×#6711yescharacteristic
280C22×D3—24no—
281C22×D3—22no—
282C22×D3—42no—
283C22×D3—42no—
284C3×Q8—24no—
285C3×Q8—24no—
286C3×Q8—22no—
287C3×Q8—22no—
288C3×Q8—24no—
289C3×Q8—42no—
290C3×Q8—44no—
291C3×Q8C2×C4×D314yescomplemented
292C3×Q8C22×Dic314yescomplemented
293C3×D4—34no—
294C3×D4—64no—
295C3×D4—62no—
296C2×C3×C4—24no—
297C2×C3×C4—24no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—21no—
304C2×C3×C4—32no—
305C2×C3×C4—32no—
306C2×C3×C4—42no—
307C2×C3×C4—44no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—122no—
312C2×C3×C4C2×C4×D312yes—
313C2×C3×C4#23512yes—
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4#23712yes—
316C2×C3×C4C22×Dic312yes—
317C2×C3×C4C2×#6711yescharacteristic
318C2×C3×C4C23×D311yescharacteristic
319C2×C3×C4C23×D311yescharacteristic
320C2×Dic3—22no—
321C2×Dic3—22no—
322C2×Dic3—22no—
323C2×Dic3—42no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—122no—
327C2×Dic3—128no—
328C2×Dic3—122no—
329C2×Dic3—122no—
330C2×Dic3—242no—
331C2×Dic3C2×#6712yes—
332C2×Dic3C2×#6712yes—
333D12—24no—
334D12—22no—
335D12C22×Dic314yes—
336C4×D3—128no—
337C3×C8—34no—
338C3⋊C8—62no—
339C3⋊C8—62no—
340C3⋊C8—122no—
341C3⋊C8C22×Dic314yescomplemented
342C2×C32#44014yescomplemented
343C2×C32C2×C4×D411yescharacteristic
344C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
345C2×C32C2×#13711yescharacteristic
346C3×D3—44no—
347C24—61no—
348C2×Q8—22no—
349C2×Q8—21no—
350C2×Q8D3×Dic314yescomplemented
351C2×Q8C2×D3212yes—
352C2×D4—32no—
353C2×D4—34no—
354C2×D4—62no—
355C2×D4—61no—
356C22×C4—21no—
357C22×C4—31no—
358C22×C4—31no—
359C22×C4—61no—
360C22×C4—184no—
361C22×C4—181no—
362C22×C4—364no—
363C22×C4C2×D3211yescharacteristic
364SD16—316no—
365C2×C8—32no—
366C2×C8—34no—
367C2×C8—92no—
368C2×C8—182no—
369C4⋊C4—32no—
370C4⋊C4—64no—
371C4⋊C4—61no—
372C4⋊C4—92no—
373C4⋊C4—181no—
374C22⋊C4—184no—
375C42—32no—
376C42—32no—
377C42—64no—
378C22×C3—21no—
379C22×C3—22no—
380C22×C3—22no—
381C22×C3—22no—
382C22×C3—64no—
383C22×C3—128no—
384C22×C3—122no—
385C22×C3—122no—
386C22×C3#91412yes—
387C22×C3#91512yes—
388C22×C3C4×#6712yes—
389C22×C3D4×Dic312yes—
390C22×C3#94212yes—
391C22×C3#94912yes—
392C22×C3C2×D3×D411yescharacteristic
393C22×C3C22×#6711yescharacteristic
394C2×D3—24no—
395C2×D3—48no—
396C2×D3—42no—
397C2×D3—42no—
398C3×C4—24no—
399C3×C4—24no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—22no—
403C3×C4—44no—
404C3×C4—62no—
405C3×C4—62no—
406C3×C4—122no—
407C3×C4C4×#6712yes—
408C3×C4D4×Dic312yes—
409C3×C4C22×C4×D311yescharacteristic
410C3×C4C2×#23511yescharacteristic
411C3×C4C2×#23711yescharacteristic
412C3×C4C23×Dic311yescharacteristic
413Dic3—22no—
414Dic3—22no—
415Dic3—42no—
416Dic3—122no—
417Dic3—122no—
418Dic3—242no—
419C32C2×#44011yescharacteristic, complemented, Sylow
420C23—62no—
421C23—64no—
422C23—122no—
423C23—122no—
424C23D3×#6711yescharacteristic
425Q8—22no—
426Q8—24no—
427Q8C2×D3×Dic314yescomplemented
428D4—34no—
429D4—62no—
430D4—64no—
431C2×C4—22no—
432C2×C4—24no—
433C2×C4—32no—
434C2×C4—32no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—122no—
439C2×C4—182no—
440C2×C4—368no—
441C2×C4—362no—
442C2×C4C2×D3×Dic312yes—
443C2×C4#380412yes—
444C2×C4D3×#6711yescharacteristic
445C2×C4C22×D3211yescharacteristic
446C8—34no—
447C8—182no—
448C2×C3—21no—
449C2×C3—24no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—124no—
453C2×C3#502614yescomplemented
454C2×C3#516414yescomplemented
455C2×C3C2×#91411yescharacteristic
456C2×C3C2×#91511yescharacteristic
457C2×C3C2×C4×#6711yescharacteristic
458C2×C3C2×D4×Dic311yescharacteristic
459C2×C3C2×#94211yescharacteristic
460C2×C3C2×#94911yescharacteristic
461D3—44no—
462C22—64no—
463C22—122no—
464C22—128no—
465C22—122no—
466C22#6393912yes—
467C22#6394612yes—
468C22Dic3×#6712yes—
469C22C2×D3×#6711yescharacteristic
470C4—24no—
471C4—62no—
472C4—62no—
473C4—122no—
474C4—362no—
475C4Dic3×#6712yes—
476C4C22×D3×Dic311yescharacteristic
477C4C2×#380411yescharacteristic
478C3—21no—
479C3C2×#502611yescharacteristic, complemented
480C3C2×#516411yescharacteristic, complemented
481C2—124no—
482C2#1059156614yesdirect product factor
483C2C2×#6393911yescharacteristic
484C2C2×#6394611yescharacteristic
485C2C2×Dic3×#6711yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C3×Q8×Dic3C2semidirect
4. C2×#63662C2semidirect
5. #10591566C2direct (N × H)
6. C2×#63575C2semidirect
8. C2×#63554C2semidirect
17. C3×Q8×Dic3C22semidirect
18. C2×C3×#215C4semidirect
28. #63662C22semidirect
29. #63575C22semidirect
31. #63554C22semidirect
34. C2×Q8×Dic3D3semidirect
52. C2×C32×Q8C2×C4semidirect
70. C3×#215C2×C4semidirect
77. C2×C3×C3⋊C8C2×C4semidirect
99. Q8×Dic3C2×D3semidirect
100. C2×#215Dic3semidirect
134. C32×Q8C22×C4semidirect
154. C3×C3⋊C8C22×C4semidirect
173. C2×C3×Q8C4×D3semidirect
174. C2×C3×Q8C2×Dic3semidirect
214. #215C2×Dic3semidirect
234. C2×C3⋊C8C2×Dic3semidirect
291. C3×Q8C2×C4×D3semidirect
292. C3×Q8C22×Dic3semidirect
341. C3⋊C8C22×Dic3semidirect
342. C2×C32#440semidirect
350. C2×Q8D3×Dic3semidirect
419. C32C2×#440semidirect
427. Q8C2×D3×Dic3semidirect
453. C2×C3#5026semidirect
454. C2×C3#5164semidirect
479. C3C2×#5026semidirect
480. C3C2×#5164semidirect
482. C2#10591566direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×Q8×Dic32
C22×C3×#2152
C2×Dic3×D122
C2×#636622
#105915662
C2×#635752
C2×#635622
C2×#635542
C2×#51643
C2×#50263